I am interested in the algebraic invariants of Legendrian sub-manifolds of contact manifolds. Here's what such objects look like. Mostly, I study the Chekanov algebra whose homology yields Legendrian contact homology and the invariants one can extracts from it. I am also interested in the correspondence between these invariants and those coming from generating families and constructible sheaves.
Geometrically, the functoriality of these invariants is seen via Lagrangian cobordisms. In low dimension, adjunction inequality leads to some applications of this relation to knot theory. In higher dimensions, studying twisted coefficients one can prove that some of those cobordisms are trvial using the h-cobordism theorem.
I am also a member of the ANR project ENUMGEOM studying enumerative aspects of symplectic and real geometry.
prépublication 2017; arXiv:1712.09126.
``Journal of differential geometry'' 114 (2020) no. 3;doi:10.4310/jdg/158337721
``Journal of symplectic geometry'' vol. 17 (2019) no. 3; doi:http://dx.doi.org/10.4310/JSG.2019.v17.n3.a2
``Annales de l'institut Fourier, Volume 69 (2019) no. 4, p. 1679-1737''; DOI:10.5802/aif.3279
``Journal of the London Mathematical Society'' Voume 100 Issue 1; doi:10.1112/jlms.12204.
Proceedings of Gökova Geometry-Topology Conference 2015, 116--150; ISBN-13 9781571463210.
Quantum Topol. 6 (2015), no. 3, 451 474; DOI:10.4171/QT/68.
Proceedings of Gökova Geometry-Topology Conference 2014, 76--113; ISBN-13 9781571463074.
Proc. Amer. Math. Soc. 143 (2015), 1325-1331; doi: 10.1090/S0002-9939-2014-12302-1.
Journal of Symplectic Geometry Volume 12 (2014) Number 3; doi: 10.4310/JSG.2014.v12.n3.a5.
Bulletin of the London Mathematical Society (2012) Volume 44 Issue 5: 981-987; doi: 10.1112/blms/bds026.
Algebraic and Geometric Topology Volume 10 issue 1, 2010; doi: 10.2140/agt.2010.10.63.
For the second semester 2020-2021 I have the responsability of the course
Logique, suites numériques et dénombrementAll information (including Zoom connections) are on MADOC..
I also give the Master 2 class on "introduction to symplectic geometry".
Here is the Zoom link to the class.
Classe notes and exercices will be given here:
Chapter 1:Hamiltonian vector fields. Exercises sheet 1. Chapter 2:Symplectic linear algebra. Exercises sheet 2. Chapter 3:Symplectic manifolds. Exercises sheet 3. Chapter 4:Symplectic reduction. Chapter 5:Generating families.
On the first semestre of 2019-2020 I gave an introduction to symplectic geoemtry.You will find here scanned notes (in french) of the class and some exercices sheets. Chapter 0:Champs de vecteurs. Exercises sheet 1. Chapter 1:Champs de vecteurs hamiltoniens. Exercises sheet 2. Chapter 2:Algèbre linéaire symplectique. Exercises sheet 3. Chapter 3:Variétés symplectiques. Chapter 4:Réductions symplectiques. Exercises sheet 4.
In 2016 I gave a mini class on contact geometry. Here are some scanned note (in french): Chapter 1:Examples. Chapter 2:Définition de base. Chapter 3:Quelques résultats de fléxibilité. Chapter 4:Structures de contact sur R^3. Chapter 5:Réduction. Chapter 6:Familles génératrices. Chapter 7:Cobordismes lagrangiens.
In 2014, I gave an advanced class on Fukaya categories. Here are some very incomplete (and probably containing mistakes) notes: Introduction to Fukaya categories.
Lagragian intersecion in locally conformally symplectic manifolds, march 15th 2021.
Invariants of Legendrian submanifolds in non-coorientable contact structures., June 24th 2020.
Invariants of Legendrian submanifolds in non-coorientable contact structures., May 7th 2020.
Invariants des sous-variétés legendriennes dans les structures de contact non co-orientables., February 21st 2020.
Invariants of Legendrian submanifolds in non co-orientable contact structure , January 22nd 2020.
Représentations de l'algèbre de Chekanov des noeuds toriques (2,m) et identités matricielles, October 10th.
Augmentations: why do we need them and what are they good for?, July 1st 2019.
Applications of Floer theory for Lagrangian cobordisms,, June 24th 2019.
Généralisation de l'identité de Sylvester et noeuds legendriens,, May 17th 2019.
Lagrangian cobordisms between Legendrian submanifolds and Lagrangian surgeries,, April 26th 2019.
Lagrangian cobordisms between Legendrian submanifolds and Lagrangian surgeries,, March 7th 2019.
Lagrangian cobordisms between Legendrian submanifolds and Lagrangian surgeries,, March 1st and 22nds 2019.
Lagrangian cocores generates the wrapped Fukaya category,, February 27 2019.
Sous-variétés lagrangiennes des variétés de Weinstein,, January 11 2019.
Twisted complexes and Floer theory for Lagrangian cobordisms,, November 26th 2018.
Lagrangian submanifolds of Weinstein manifolds, October 19th 2018.
Categories associated to Legendrian links I et II, September 21st et October 26th 2018.
Categories associated to Legendrian links, June 11th 2018.
Générateurs de la catégorie de Fukaya d'un secteur de Weinstein,, January 19th 2018.
Chirurgies lagrangiennes et complexe tordus en homologie de contact legendrienne, November 23rd 2017.
Intersections lagrangiennes dans les fibrés cotangents conformément symplectiques, November 14th 2017.
Catégories associées à une sous-variété legendrienne, October 20th 2017.
Conformal symplectic geometry of cotangent bundles, June 13th 2017.
Isotopies legendriennes positives et homologie de Floer, March 3rd 2017.
Obstructions à l'existence d'isotopies legendriennes positives, January 19th 2017.
Isotopies legendriennes positives et homologie de Floer, December 13th 2016.
Positive Legendrian isotopies and Floer theory, November 2nd 2016.
Isotopies legendriennes positives et homologie de Floer, October 21st 2016.
Restrictions on the topology of Lagrangian cobordisms, April 25th 2016.
Positive Legendrian isotopies and Floer theory , Apris 6th 2016.
Positive Legendrian isotopies and Floer theory , March 22nd 2016.
Non commutative augmentation category , March 7th 2016.
Restrictions on the fundamental group of some Lagrangian cobordisms. , Febraury 11th 2016.
Legendrian contact homology and positive isotopies , February 5th 2016.
Legendrian contact homology and positive isotopies , December 16th 2015.
Legendrian contact homology and positive isotopies , November 9th 2015.
Legendrian contact homology and positive isotopies , October 13th 2015.
Legendrian contact homology and positive isotopies , August 28th 2015.
Positive Legendrian isotopy and Floer theory, June 12th 2015.
Sur la topologie de endocobordisme lagrangiens, May 21st 2015.
On the topology of Lagrangian endocobordisms, March 27th 2015.
Sur la topologie des endocobordismes lagrangiens, March 12th 2015.
Sur la topologie des endocobordismes lagrangiens, March 3rd 2015.
Sur la topologie des endocobordismes lagrangiens, February 16th 2015.
Floer thoery for Lagrangian cobordisms and topology of Lagrangian endocobordisms, December 16th 2014.
Floer thoery for Lagrangian cobordisms and topology of Lagrangian endocobordisms, 2014 July 23rd.
Floer theory for Lagrangian cobordisms-2: applications., 2014 May 29th.
On the topology of Lagrangian cobordisms between Legendrian submanifolds, 2014 March 17th.
Floer Theory for Lagrangian cobordisms., 2014 February 21st.
Floer Theory for Lagrangian cobordisms., 2014 February 18th.
Lagrangian Floer Theory for Lagrangian cobordisms., 2013 December 10th.
Lagrangian Floer Theory for Lagrangian cobordisms., 2013 November 8th.
Théorie de Floer pour les cobordismes lagrangiens., 2013 September 26th.
Homologie de contact legendrienne bilinéarisée et catégorie d'augmentation., 2013 September 18th.
Théorie de Floer pour les cobordismes lagrangiens., 2013 April 11th.
Bilinearised Legendrian contact homology and obstructions to Lagrangian concordances., 2013 March 1st.
Homologie de contact bilinéarisée et obstruction à l'existence de concordances lagrangiennes., 2013 February 26th.
Sur la non-symétrie de concordances lagrangiennes, 2012 December 14th.
Constructions de cobordismes Lagrangiens et tranches non-colliésables de surfaces Lagrangiennes., 2012 September 28th.
Homologie de contact legendrienne bilinéarisée., 2012 March 9th.
Bilinearised Legendrian contact homology, 2011 November 16th.
Example of non-collarable slices of Lagrangian surfaces, 2011 October 25th.
Bilinearised Legendrian contact homology, 2011 October 25th.
Constructions of Lagrangian cobordisms and non-collarable slices of Lagrangian surfaces, 2011 September 12th.
Lagrangian cobordisms of Legendrian knots and applications, 2011 March 2nd.
Cobordismes lagrangiens de nœuds legendriens, 2009 November 5th.
Non-symmetry of Lagrangian concordances, 2009 January 31st.
Non-symmetry of Lagrangian concordances, 2008 October 10th.
Sur la non-symétrie de concordances lagrangiennes, 2008 April 30th.
Cobordismes lagrangiens entre nœuds legendriens, 2008 January 11th.
Lagrangian cobordism of Legendrian knots, 2007 October 15th.
Cobordisms of Legendrian knots, 2007 March 26th.
Concordances lagrangiennes, 2006 February 7th.
Concordances lagrangiennes des nœuds legendriens, 2005 May 16th.
This workshop will lead to a restitution by the students in April.
With MAOTIK we gave a conference on relations between and arts and sciences in Stereolux during the "nuit blanche des chercheurs 2021" in Nantes.
I am the local organiser in Nantes of the 5 minutes Lebesgue , some series of 5 minutes talks on mathematics for a various audience (unfortunately on break at the moment).
I supervised several workshops MATHh.en.JEANS